Try a button down shirt on top of a tank top, or slash holes in a t - shirt and wear a loose shirt on top. (amotherinisrael.com)
This also allows you to cover the screen top of your tank with a piece of glass, plastic or wood, thus capturing your humidity. (petbusiness.com)
Wear a simple long coat on top of your tank tops, you can also close the front button of the coat if you want to hide the shirt that you are wearing underneath. (outfittrends.com)